Speaker
Michael Tannenbaum
(Brookhaven National Laboratory (US))
Description
Total charged multiplicity distributions, $P(N=N^+ + N^-)$, in p+p collisions and A+A collisions cut on centrality are well fit by Negative Binomial Distributions (NBD). Recently it was found that the individual $P(N^{+})$ and $P(N^-)$ distributions in PHENIX are also well fit by NBD. A theorem from Quantitative Finance states that for integer valued Levy processes such as the difference between two Poisson or two Negative Binomial Distributions, the cumulants $\kappa_j$ of $P(N^+ - N^-)$, the difference of samples from two such distributions, $P(N^{+})$ and $P(N^-)$ which are both Poisson or NBD, with cumulants $\kappa_j{^+}$ and $\kappa_j{^-}$ respectively, is the same as if the $P(N^{+})$ and $P(N^-)$ were statistically independent, i.e. $\kappa_j=\kappa_j^+ +(-1)^j \kappa_j^-$, so long as the distributions are not 100\% correlated. This was tested and verified with the PHENIX measurements of $P(N^+ - N^-)$, $P(N^{+})$ and $P(N^-)$ from central (0-5\%) Au+Au collisions at $\sqrt{s_{NN}}$ from 7.7 to 200 GeV, leading to simplified calculations of the measured ``raw'' cumulants, their statistical errors and the Binomial efficiency corrections. Applications to acceptance corrections, which are complicated by correlations in both $\delta\eta$ and $\delta\phi$, will also be presented.
| On behalf of collaboration: | PHENIX |
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Author
Michael Tannenbaum
(Brookhaven National Laboratory (US))
